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The Euler-Lagrange equation is a fundamental result in the calculus of variations, widely used in quantitative methods, physics, and optimization problems. It provides a necessary condition for a functional to attain an extremum, usually a minimum or maximum. A functional is a mapping from a space of functions to real numbers, often expressed as an integral of a function called the ______ _________ ______ ___ ______ _____ _______ ________.
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